Basic properties
| Modulus: | \(4900\) | |
| Conductor: | \(1225\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(105\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1225}(81,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4900.dc
\(\chi_{4900}(81,\cdot)\) \(\chi_{4900}(121,\cdot)\) \(\chi_{4900}(221,\cdot)\) \(\chi_{4900}(261,\cdot)\) \(\chi_{4900}(541,\cdot)\) \(\chi_{4900}(641,\cdot)\) \(\chi_{4900}(681,\cdot)\) \(\chi_{4900}(781,\cdot)\) \(\chi_{4900}(821,\cdot)\) \(\chi_{4900}(921,\cdot)\) \(\chi_{4900}(1061,\cdot)\) \(\chi_{4900}(1241,\cdot)\) \(\chi_{4900}(1381,\cdot)\) \(\chi_{4900}(1481,\cdot)\) \(\chi_{4900}(1521,\cdot)\) \(\chi_{4900}(1621,\cdot)\) \(\chi_{4900}(1661,\cdot)\) \(\chi_{4900}(1761,\cdot)\) \(\chi_{4900}(2041,\cdot)\) \(\chi_{4900}(2081,\cdot)\) \(\chi_{4900}(2181,\cdot)\) \(\chi_{4900}(2221,\cdot)\) \(\chi_{4900}(2361,\cdot)\) \(\chi_{4900}(2461,\cdot)\) \(\chi_{4900}(2641,\cdot)\) \(\chi_{4900}(2741,\cdot)\) \(\chi_{4900}(2781,\cdot)\) \(\chi_{4900}(2881,\cdot)\) \(\chi_{4900}(3021,\cdot)\) \(\chi_{4900}(3061,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 105 polynomial (not computed) |
Values on generators
\((2451,1177,101)\) → \((1,e\left(\frac{2}{5}\right),e\left(\frac{2}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
| \( \chi_{ 4900 }(81, a) \) | \(1\) | \(1\) | \(e\left(\frac{94}{105}\right)\) | \(e\left(\frac{83}{105}\right)\) | \(e\left(\frac{22}{105}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{61}{105}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{2}{105}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{13}{15}\right)\) |